Change PDE to normal form

Hi I have this problem
Reduce to normal form the following equation
x2d2f/dx2-y2d2f/dy2=xy.

First I guess by normal form , they mean a more standard equation, for example Laplacian.

I usually know what to do when the coefficients are constants, but in this case I dont know.

I think it is possible to transform this into a Laplacian
, because we haven't seen the wave equation.
So I tried to do a change of variables, and to get the Laplacian I need to solve a system of four differential equations, do you think this is the way it should be done or there is an easier change of variables I should try.